The Polish gift 

The single most important thing to know about breaking Enigma is that Britain did not start from nothing. Poland got there first, years earlier, and with far fewer people.

In 1932 the Polish Cipher Bureau put a young mathematician named Marian Rejewski on the problem. This was itself a departure. Cipher work had traditionally been the province of linguists. Rejewski, working with intelligence material supplied by the French, reconstructed the internal wiring of the German military Enigma using group theory, essentially deducing the shape of a machine he had never seen from the mathematics of its output. It remains one of the outstanding feats in the history of cryptanalysis.

With Jerzy Rozycki and Henryk Zygalski, Rejewski then built practical methods for recovering daily settings: catalogues of rotor characteristics, perforated sheets that let a clerk find matches by stacking paper over a light, and an electromechanical device called the bomba that automated part of the search. Through most of the 1930s Poland was reading German Enigma traffic.

Then the Germans changed the machine and the procedures, adding rotors and plugboard connections. The Polish bureau's methods, built for the older configuration, could no longer keep pace with the resources available in Warsaw. And by mid-1939 it was clear what was coming.

In late July 1939, at a meeting in the Kabaty woods near Warsaw, the Poles told their British and French counterparts everything. The wiring. The methods. The Zygalski sheets. They also handed over reconstructed Enigma machines, one of which reached London. Five weeks later Germany invaded Poland. The cryptologists escaped through Romania to France, and continued working in exile.

It is difficult to overstate what this changed. Britain arrived at the problem already knowing the machine's internal structure, already holding a working attack, and already knowing the thing that is hardest to know in intelligence work: that success was possible. Everything Bletchley built in 1940 was built on that foundation, and for decades after the war the Polish contribution was barely mentioned in English-language accounts, partly because the whole subject was classified and partly because of who was writing the histories.

What Britain added was scale, industrial organisation, and a new mathematical idea for defeating the strengthened machine. That idea came from a twenty-seven-year-old Cambridge fellow who had already, before the war, written a paper about imaginary machines.